浙江省杭州市2022-2023学年新高三暑期阶段性测试数学试题【含答案】

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14J%>%>iL/(ᑘ+/(O)>/(Q)-/3)ᡂS,ᓽ32>U2ᡂS.W+xX-xxX]2]22Z7/ஹfMX2Inx/,/ஹ-2x(x-l)1-lnx['(\=42=+(,hr(x)=——ᜧ(ᓝ——,xe-xxex/?'প=l>0,ᡠ8xe(l,x0),“(x)>0ᦑ஻(x)=/dᙠ(1,X஺)eᓫ3⌴fXᡠ8/>᳝>O>1hᡂS.X2iᦑ⌱jBC.13.180ூᑖ᪆௃ᑏqr⚗stuv⚗wuᵫyᨵGz⚗r⚗u{ᦪᨬᜧ}~஻ᦪ⚗.ூ௃"-50»=(-2YCKᵫ⚪1huyᨵ(,஻=10(Cj=cj).lCj2Cj’10-5r-----=0,r=2,2ᡠ8ᦪ⚗i(-2)2,=180.ᦑ180.ூᑖ᪆௃᪷ᩩ9ᓄu~q/--=1,}qᦪᑡḄv⚗wuᓽ~ᦪᑡ4Ḅv⚗wu}qᦪᑡ,Ḅv⚗wu(}qEᫀᓽ.ூ௃.•.%+d=1♦,U=l-a“!4|=1-4ᔣ.%((ᔆ(l+*(-,,ᔆ1+%-1%EᫀG8⚓ᐳ21⚓

151஺஻(——=0,ᓽj%e8✌⚗i2,w©i1Ḅ©ᦪᑡ,—=2+(஻-l)xl=“+l,—!—ann+\1111n..b=l-a=1-----=----nn஻n+1n+l.h-2023…2஺”-2024•2023ᦑEᫀi5ூᑖ᪆௃᪷/(xJ=l+21nr,g(X2)=/~ᑮ°=(X|-l)e'L'>0,r=e,nX2-lnx>0,ᵫy=x-e*ᙠ2InfIn/Inf0+8)1ᓫ3⌴f~ᑮIn%=%-1,~ᑮ-------=²!—=-Fᑭᵨ¶ᦪ·}.x,x-X,x-Inxt222ூ௃ᵫ⚪/(xj=X]+ln(_C1-1)=1+21n~Wߟ1+ln(_x,-1)=lnᡠ8In[(»(l)ev'-']=ln?,ᓽr=(i(ige>0,¼8(%)=஽111%2=¾,~¾=e'"X2-Inx,>0,[y=A>e",ᑣy'=(x+l>e*>0ᙠ[0,+8)1ឤᡂS,ᡠ8y=x•e”ᙠ[0,+00)1ᓫ3⌴fᡠ8111Â2=Ã(1,ᑣx/lnx2=l,InfIn/Infᡠ8-------=-;—=-TX\X1~X2X2,X2t[/!«)=Ç(t>0),l-21nrᑣ஻'Q)ᡠ8/2rᙠoeÊ1ᓫ3⌴fᙠ/,+81ᓫ3⌴5,EᫀG9⚓ᐳ21⚓

16niᡠ8஻Ì2?=஻e2=—.I2eᦑh2eᵫÍ?PᙠÏᙊ1ÑÒOPÇxÔḄÕᔣḄᜳ×ᙠØᡠ8ᐜÚNFOQ=஺¼ᵫccos20ccos6sin6~FQOP=Q,0Ü802஺Ý05Ḅ11᜛)ß~Pj?᜛ᙠÏ~—~ᙊ1ᡠ8ã?PḄᙶ᪗æᐭÏᙊÕèéᓄê~ëì.ூ௃Ú|Ofj=c,P(x,y),ZFOQ=0,íijQk'cos?accosOsin®),uuuixw(0rcossinf)ᵫOQ=2OP(4ñ0),MPuòg,æᐭÏᙊÕèI/X)~ᙠó+ôõ£=ᑖ÷£,ᓄê~4ñÇ_(0஺÷஺÷90஺)ឤᡂS,a~b~a~a-l+cos-6ᵫ~ø!,ᓽa222c2,ᦑee[o,ø.⚪ὃúḄeᑭᵨÏᙊéûᐵý=?Ḅᐵ{}þÿ᳛
ᔠឋ
⚪.7217.(l)cos2a=--,tan(/3-a)=—7F(T)a=P=-ூᑖ᪆௃(1)ᵫ#$ᐵ&'ᖪᦪᐵ&ᓽ+,-cos2«/ᵫcos01ᔠ#$ᐵ&,-sin2a,34,-tan2a,5ᳮ,-tan(a+஻)
9ᵫ:ᑗ<=>?,@tan(/?-a)ᓽ+/BᫀD10⚓
ᐳ21⚓

173(2)ᵫ3஺+85஻-3(2+I)=J1ᔠ#$ᐵ&'KLM=>?ᓄO-/(sina-sin0N+g[(cosa+cos4PQ2(cosa+cosZ?)+l]=0,34-ᑮsine-sin4=0'cos6z+cos/?-l=0,ᓽ+,@a'4ḄT.i_16/.ஹ4c.ocosVa-sin2a1-tan2aQ7c2(1)tan«=—,W.cos2a=cosa-sin~a=——--------------=-------------=——=------,Q஺
3cos“a+sina1+tana]+Y25~9/24ZY┦=
ᓽ.,.2eze(0,^-),2+/7£(0,4).sin2a=Ji-cos?2a=—,sinla24“ஹ/ஹ/ஹP..tan2a——=~/(x)=cosx,/(2+᜛)=cos(a+᜛)=—sin(a+᜛)=Jl-cos2(a+/?)tan(a+6)=^Q2,,ஹ_249+/_\/ஹtan(a+Z?)-tan2a72,7/.tan(y0-cr)=tan(«+/?-2«)=-----/——J-------=------Q.b
cos2a=------------,')'y)l+tan(a+^)tan2a^iH25i+2x72tan(^-a)=—/ஹஹ3/3(2)••/(a)+f(0)-f(a+0)=Gcosa+cos(3-cos(a+,cosa+cosp=g+cos(a+஻)=g+/cin?a+cos?a)+gcin,᜛+cos2/?)+cosacos/?-sinasinp=/+g(sina-sin/3)2+J(cosa+cosy?)2,ᡠe/(sina-sin/?)2+|^(cosa+cosp)2-2(cosa+cos1)+1]=0,ᓽg(sina-sinQ+(cosa+cosp-1)2=0,.*.sina-sin[3=0JI.cosa+cos/7-1=0,fQa,Iᐔ/7Gg0,4h
i஺=Ij
cosa=cos>0=—,:.a=/3=—Si஺^kQ$j
cosa=-cos4lTTcosa+cos£—l=0mno
Jpᔠ⚪q.bᡠr
஺=᜛=1.18.প஺஻=2"-1(2)(n-l)-3,,+lூᑖ᪆௃BᫀD11⚓
ᐳ21⚓

18g1htuvwᦪᑡḄyz{|},@~
9,@ᡭ
34tuv<ᦪᑡḄyz{|},@%;g2h1ᔠg1h,tu┯m,-Bᫀ.g1h%Ḅ>wY4,ᡠe=3"T,ᑣ"14=4=27,ᓽq=]+13d=27=d=2,ᡠe4=1+2g“-1h=2“—1.4g2hᵫপC,,=g2"-13"T,6Ḅ஻⚗MY
ᡠeS,,=g2*1-13஺+g2*2—1c31+g2ஹ3-1c32+...+g2஻-1h-3'1……জI¡3S„=g2xl-lh-3,+g2x2-lh-32+...+g2n-3h-3n-1+g2n-lh-3"……ঝ
জ-ঝ
-_2S,,=l+2g3i+32+—+3"Th—g2஻—lh.3"=g2—2஻h.3"—2,ᡠeS“=g஻T3"+1.19.g1hᑖ§ᑡ¨᪆/g2hgihᑖ§ᑡ¨᪆/giih©ª¨᪆.ூᑖ᪆௃13g1hᵫ⚪«
¬⍝⚪®B¯Ḅᭆ᳛Y:
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9ᵨ┯mMJ34-1v?ÚÛ-EgᓃhÕ/+1+g£|+g£|+…+g
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-2ூÝ௃BᫀD12⚓
ᐳ21⚓

19x/(%=l,2,3),P(X=4)(I)P(X=%)=44ÞßX”Ḅᑖ§ᑡYX,12343927P4166464(2)(i)j
D4ÁÂB¯D^⚪,á☢4-1Á®ãᨵQÁB¯D--⚪
ᐸᭆ᳛Yp.ᐸᭆ᳛Yá☢4-1ÁᨵQÁB¯DQ⚪,ᦑWᓄ=A)=P/+P/=«£|iᓃ=஻j,á☢஻-1Á®ãᨵQÁB¯DQ⚪
ᐸᭆ᳛Yp“=(;á☢”-1ÁᨵQÁB¯DQ⚪
ᐸᭆ᳛Yp;,ᦑZᓄ=஻)=%+ᶪ;=("+1)(1.ᓃḄᑖ§ᑡY123n-ln("1)(3(஻+l)(3P2æᕖ1BᫀD13⚓
ᐳ21⚓

20(ii)E(ᓃ)=£>()+஻(஻+1)@(”wN*,"N2).1E(K)-E(ᓃ)=஻2@+(஻+1)(஻+2)@-஻(஻+Î)=("+2)@>0,ᦑEᓄ)0,ᦑEᓄ)

2120.(I)*+᪆,(II)-.25ூ*௃(I)ᵫ2345஻=252)=2.38ᓽḄ:;T=>஻V,ᵫNBPC:;3m஻3CTN=-BC=2.2TADHBCᦑ77V4”,JKL4WNTBNOJKLPMV஻AT.SB஻uN☢E43MV(ZN☢X43ᡠZMV஻N☢X(II)83cḄ:;E=\ZE.ᵫ55=d஺4dEJLBCbcdJ_dDgAE=JAB2-BE7=h2-j)2=kZABᙶ᪗n;oḄpᔣBXstpᔣuv᝞xᡠyḄz{|}ᙶ᪗~.ᵫ⚪3ẑ0Q4),"(020)஺(620)(12)2——■—■J5ߟ■JsPM=(0,2,-4),P7V=(—,1,-2),AN=(t,1,2).22”=(x,y,z)BN☢RVWḄᔣᑣn-PM=0,2y-4z=0,ᓽn-PN=0,-^-x+y-2z=0,877=(0,2,1).,—.

22-AN\xஹPMீ஻,=✌ᫀ15⚓ᐳ21⚓

23pூὃ௃z{☢{ḄNOᐵ~z{ᔣ☢}.ூᢈ;௃1
¡¢v£¤¥:ḄNOᐵ~¦¦§¨NOᩭª«cNO¦¦ᑭᵨ®}LḄ:¯ஹNOJKL°LḄNOᐵ~ᩭ±¡,²2
z{:Ḅ}³´µ¦¦§¨uvz{|}ᙶ᪗~ᑭᵨz{ᔣ:Ḅᜳ}´µᩭᜐᳮ.21.1
—+/=142
+᪆ூᑖ᪆௃13τ—+-----11
ᵫ234¹a24b2,4¹a2=4,^=1,ᓽºᙊEḄp¼,a2-b2=32
⌱জᑣ2,0¿,B²2,0¿,kNA=77^=W'"N5=■-=TᡠZLA:Á=W8X+2;,/N§:y=-rx-2
,14-Z31-ZJὶv|³ºᙊḄp¼P,஺Ḅᙶ᪗ÃÄ4ᑮ|PQḄp¼Æy=0,x=4,ᦑ|Ç஺ឤ¨É;²4,0¿.⌱ঝᑣMS,2;,C80,1;,080,-1;,p²Ë¿,Q²%%
,,2-11,2+13,13,ceiu=-----=_^ND=------=_ᡠZ¹y=_X+1,/9¹y=_X_15sssSSὶv|³ºᙊḄp¼P,஺Ḅᙶ᪗ÃÄ4ᑮ|PQḄp¼Æx=0,y=,,ᦑᫀ16⚓ᐳ21⚓

24|PQឤ¨É;²1¿ᵫ23C=6,;ᙠºᙊÏᡠZ5+Ñ=1ÒSB/b=஺2,ᡠZa2=4,b2=1»ᡠZºᙊḄp¼B.a?=4,b=1²2¿⌱জ,ᑣ᪷Ø⊈ÚÛÜÝ"ß³Áàá,ᵨ¿,k/==T,NA1+231—2y=*+2¿ᡠZ3¹y=g²x+2¿,஻¹y=T²x-2¿,,äåy4¹-+/=114'²9+4/2¿X2+16/2X+16/2-36=0,A=256r-4²9+4஻¿06é-36¿=362>0ᡠZ16ë-36-8ë+18ᑣ“î-8r+18ফ]-2.Xp>ᡠZX஺=ᡠZP9+4/9+4/9+4ᡝ'9+4/)y=-f(x-2)f,äåy4¹(l+4r)x2-16rx+16z2-4=0,—+V=14ô=256/-4(1+4316--4)=16>0,ᡠZ2%=$WᡠZ&=ø|,ᑣ%=£*ফ4tᡠZQp¼BᡠZy=0,x=4,ᦑ|P஺ឤ¨É;(4,0).⌱ঝ,ᑣMS,2),C(O,1),£>(O,T),஺(/»)஺(4B)UV-—W=-ᕜY=--ý°,ᡠZ&C:y='ÿ+1,/9y=-x-],SSSSSSy=-x+i,ஹSy(4+1)y2+2s2y+s2-4=0,A=4(4+1"s?-4)=64>0ᡠ—+/=14$2—4gஹ]-8sᓃ#…/-8sr_4)36—/ᓃ#…24sy=———(ᡠ)=~~;(ᡠPf-7,ߟ—70ᳮ=—~n(ᡠ~(P0/+4/+4+42+4j52+36Q/+3655ᫀ717⚓(ᐳ21⚓

2536-52S2-424636-?"(.?+12).(12-.s2)_52+3652+4)=ᡠ>?@஺ḄCᡠQkpQ?+36\2+36,24s-8s16s9+12)S2+36"?+4c2-412-528s12-52+2r-8S2+4iEFy-KTwA+?+4Jx=0,ᑣM2d+4)=OP=5ᦑ>?PQឤTUV(o,£|.ᐵ[VV\]⚪ὃ`aᙊCEḄcd(ὃ`>?)aᙊḄefᐵg(ὃ`hijk(l⚪Ḅᐵ[mcnP(QḄᙶ᪗(qrᑮ>?@஺ḄCE(ᓽun>?PQឤTḄUV(vwx⚪.22.(1)(i)yz{l᪆}(ii)yz{l᪆}(2)(i)yz{l᪆}(ii)4ூᑖ᪆௃(1)(i)ᵫ⚪g(x)=]n(x+i)(q᪷⚪(qyzᓽu}(ii)᪀⌼ᦪ(()=+,2-2+|(F(X)=/(A)-/7(X),᪷F(x)Ḅᓫឋf(x)>H(x),qᵨ"(x)஻x),J”(x)+ar—b=0,ᑣ.ಘ1,|0,qx“=e*(ᑭᵨᦪ³´µdyzx“=e(ᡂ·(qyz¸%¹Fºᦪᑡ;*=1-/c½)="(ii)ᵫপ,P=1E&)=k+l-k(l-p)",qªE4)>E&Wnk>Sk,᪀⌼ᦪ஻x)=lnx-gx(x>0),Ẇ¿ᦪḄᓫឋᓽu5ᫀ.ூ௃l(I)পÀF½)=(ÁÂ(Á)+2,2,5ᫀ718⚓(ᐳ21⚓

26/ஹxln2ᡠ(gÃxÄ=i^(/X/Xf\mil1ᑣ—+—7-;+…+-------;----------[gপ+1ÅgÃ3Ä+3j[gÃ21Ä+2lJ12345xÆ—|-------1------1------------1-----------F••H------------------29285Ã24-l
6Ã25-l
Ã2X-1ÄÃX+1Ä<0.85+~~7r+-7r+…+------r-------5Ã24-l
605-1
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x+l
111<0.85++5+..(+24-l2-l2-<0.85+*+/+…+Ç=0.85+1x11<--10UÃ1
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+2,Ê10yË.(ii)᪀⌼ᦪ஻("=(+,2-4+|,@(x)=/(x)-"(x)ᵫw?Ì=2/2+;⊈P+ᔁ(2ᙠ(T,+8)Ðᓫ⌴ÒÓx7▬(F'x
->0ᡠ@(x)ᙠ(-1(0)Ðᓫ⌴Õ((0,+8)Ðᓫ⌴Ò(ÓX->00Ö(F(x)->0ᡠ@(x)>F(O)=O,gpy(x)>H(x).ᵫwᢣᦪÒØÙ᳛ÛᜧwÝ+£஺Þ0,”>0)ßàḄᦪ(ÓX-0HÖ(@(x)-0.ᦑuᵨ”(x)/(x)J"(x)+ar-b=0,ᑣáâ<᧕0<ä<å2,ᑣ½æçèᓝêᔣ<$-+ln265ᫀ719⚓(ᐳ21⚓

27e25)Tbe—A,_o?.|Z?Xj-bx\<6b“2-3¦+4<24\Jb2-3b+4211rr(II)(i)yzª஻=2«(e—=e3,Jg=ÆÆ”>0,ᑣgw1,ì᳝.X=1,•.ï☢yzñòḄó᦮ᦪ½x=eᔉ.nজª”=1,2«(÷ᯠᡂ·}IkঝᎷûñòḄ஻=%«(x«=eü(ï☢yz஻=ᦇ+1«(&+[=©3k2ஹkk2ká•4+1=”ᡈ/+1=-e*3(ÿ
','=”ᡂ•ᵫজঝ஻ᦪᑡv.x=en(ii)ᵫ(i),⌲!"Ḅ$ᨵ᝕,ᡠ(E&)=k,)!ᓰ2Ḅ+,+1,.=1!/0Ḅ124)34Ḅ56ᙳ▢ឋᦑP©=1)=(1-P)«A"=&+1!/0Ḅ12஽)34Ḅ56ᙳ□ឋᦑE©="+1)=1-(1-0஺E(^)=(l-p/+(^+l)[l-(l-p)i]=^+l-A:(l-p)i2)E«)>EC)gHk>k+\-k^-p)k,ᓽ=(ᓝ)KᫀM20⚓ᐳ21⚓

28112-Y:Ank>-k.P/(x)=lnx--x(x>0),=—~,••XN3!r(x)<0,ᓽ஻x)ᙠ_3,+8)aᓫcd.4gIn4al.3863,—q1.3333,345In4>—Aln5«1.6094,—®1.6667,33|a5/.In5<-.3kḄᨬᜧ4.r⚪ὃuᑭᵨxᦪẆz{ᦪḄᨬ|}~Ḅᦪᦪὃuᳮ⚪.r⚪M⚪Ḅᐵᙠ〉Ḅᵨ~Ḅ,¡¢M£⚪Ḅᐵᙠᐜ¥¦஻=2!q=¨=1>0,%=e?¬ᑭᵨᦪ|}KᫀM21⚓ᐳ21⚓